Integration with series.

05172021, 10:54 PM
(This post was last modified: 05182021 12:40 AM by t_angenbrandt.)
Post: #1




Integration with series.
The CAS does not detect that a series is 0 for the PDF of the binomial random distribution above k=n, so there are some simplifications that can be made with this assumption;
I use the following program to calculate the variance in the valuedomain: Code:
The program is limited for binomial distribution that has been defined as a continuous function using Dirac(): It is basically identical to the usual schoolbook definition, but extended for a continuous argument. Code:
When this function, s_pdf_binom... is applied to s_var(), I get an integral as an answer (indicating that CAS could not integrate it). Example: Code:
Now here is what I want: How can I get some hint from the CAS, that it has failed to integrate something or has done something else that does not give me a desired result? One obvious way is simply by looking for "integrate" or "∫" characters in a string that is returned when integration is complete so that the program can then take a different approach to get the CAS to return a useful result. But is there a more elegant solution like some function I can call to check for CAS behaviour without assuming the variables all the time? (Not important but for the interested ones: for this example one might take the fouriertransform and evaluate it at s=0 for the mean value. The CAS perfectly works with this approach, but it takes sometimes a long time to calculate, so it is not always desirable.). 

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